This invention generally relates to tuning musical instruments and more specifically to a novel method for tuning certain musical instruments.
Conventionally, a person tuning a musical instrument listens to a reference note and adjusts the instrument until its corresponding note seems consonant with the reference note. Consciously, or not, the person tunes a note for a specified beat rate, (which may be zero beat), with the reference note, usually at some harmonic of either one or both the notes.
This type of tuning is possible because an equally tempered scale is based upon simple mathematical relationships. In practice, however, pianos and other stringed instruments do not follow simple mathematical rules. In fact, piano tuners and builders use "harmonic" to denote a mathematical harmonic of a note and "partial" to denote the overtone which the string actually produces. The difference between a harmonic and a corresponding partial is caused by "stretch". Stretch is significant. In a piano, for instance, the second partial from a string may average 2.002 to 2.006 or more times the fundamental frequency (i.e., the first partial). Thus, if the fundamental notes are tuned mathematically, stretch causes the piano to sound out of tune.
Therefore, pianos and similar instruments must be tuned differently. Historically, a piano tuner uses a complex, iterative aural process in which he tries to reduce errors to a minimum step-by-step. Basically, he starts tuning a piano in a "temperament octave" by adjusting a first note to a reference frequency, usually provided by a tuning fork. He adjusts the remaining notes in the temperament octave by listening to partials of notes in third, fourth and fifth intervals. For example, in striking an interval of a third with a previously tuned lower note, the tuner adjusts the upper note while listening to the beat between the fifth partial of the lower note and the fourth partial of the upper note. He assumes the proper relationship exists when he hears a predetermined beat frequency.
Listening to these partials and beat frequencies reduces errors at the fundamental frequency because the partials multiply any error in terms of actual frequency differences. That is, a 4 Hz error at the forth partial represents only a 1 Hz error at the fundamental. Also, the use of partials inherently tends to compensate for piano stretch. However, the process is not perfect because the tuner's beat rates are calculated from harmonics rather than partials, and the tuner usually checks the temperament octave by retuning it using different intervals to minimize the tuning errors.
Once the tuner completes the temperament octave, he tunes other notes by comparing partials of notes at octave intervals. He may, for example, listen to the beat between the fouth partial of a lower, tuned note and the second partial of the upper note while adjusting string tension for the upper note. Lower notes are tuned similarly, although not necessarily with octave intervals.
Each note in a piano is sounded by striking two or three strings. During the foregoing procedure, the tuner damps out strings so only one string actually sounds when a hammer strikes all the strings associated with that note. After the tuner completes the procedure, he must tune the other strings for each note by comparing either the fundamental or partial frequencies of two strings associated with a given note.
As may be apparent, however, the entire procedure requires that a note sustain long enough to enable the tuner to determine the beat frequency. Obviously, the longer the interval the note sustains, the more accurately the tuner can determine the beat frequency. In tuning, each note struck sounds until it dies out naturally or the key is released. By "dying out", I mean that the note can no longer be heard. Thus, the time the note sustains limits the accuracy of aural tuning methods.
Although there are several tuning aids, no one aid has wide acceptance. In one, a high frequency oscillator produces an output clock signal at a selected frequency. A series of frequency dividers and an octave selector switch provide a means for generating a reference signal at a selected subharmonic frequency. The tuning aid combines this reference signal and a audio signal representing the note being tuned either to generate an audible beat note or to deflect a pointer on an indicating meter. Unfortunately, these aids lose accuracy as the tuned note comes into frequency with the reference. When the beat rate decreases below 20 Hz, the audible beat note becomes inaudible. Similarly, an indicating meter uses a frequency-to-current converter so the current level goes to zero at a zero beat. As the current approaches zero, the visual indication becomes less accurate. Both types of display, therefore, lose accuracy at the very time it is most necessary.
In another unit, the tuner attaches a piezoelectric transducer to a particular string or a sounding board to produce a corresponding electrical signal that is applied to the vertical deflection plates of a cathode ray tube. A selector switch, crystal controlled oscillator and a series of frequency dividers generate a selected reference signal which energizes the horizontal deflection plates of the tube. In using this circuit, one apparently assumes, erroneously, that a piano generates a constant, repetitive wave form. In fact, a piano string generates an extremely complex wave form comprising a fundamental tone and wide range of partials, often of the same magnitude, but slightly out of tune with each other. Furthermore, many of the component frequencies are not necessarily constant in magnitude because a string vibrates in many modes, each with its own damping constant. These factors cause the waveform to change continuously, so the display is difficult to interpret.
Another problem relates to dynamic response. Initially, the amplitude of the signal is sufficient to drive the display off the screen. As the tone dies out, the input to the vertical deflection plates falls below the minimum level necessary for generating a usable display. An obvious solution is installing a variable gain amplifier to maintain the output at a constant value. However, a circuit which provides satisfactory results over the wide range of conditions and waveforms which the piano generates is difficult to attain in practice. If the variable gain circuit actually tracks the decay, it may follow the wave-form and provide a dc output signal. Therefore, this solution is not practicable especially in view of the non-linear parameters or conditions and the short interval for a readable display. This effective dynamic range further complicates tuning because adjusting a string while monitoring the display is very difficult.
Still another tuning aid receives the audio signal from a piano and generates a corresponding electrical signal to energize the blanking or Z axis circuitry of a cathode ray tube. A circular generator energizes X and Y axis deflection plates with a reference frequency so the electron beam describes a circle on the screen. If a note is in tune with the reference, the audio signal blanks and unblanks the electron beam during the same part of each revolution to thereby display one arcuate segment. A second partial input signal produces two such arcuate segments; a third partial input signal, three segments; and so forth. If a given note is not exactly harmonically related to the reference, the segments rotate. The direction of rotation indicates whether the note is sharp or flat while the speed of rotation indicates the difference in frequencies. As notes in the upper piano produce a display with a number of segments, the spaces between adjacent sectors diminish; and the absolute frequency deviation which produces a persistent display tends to decrease. Furthermore, alternately blanking and unblanking the beam produces an indefinite segment termination on the screen. When the frequency deviation is small, the indefinite termination makes it difficult to determine whether the edges of the segments are moving. When notes in the lower range of the piano are tuned, the tuner must try to adjust while the tuning aid responds to partials, since subharmonics of the reference frequency generate complete circles on screens.
A tuning aid must provide some means for stretch compensation when it is used to tune a piano. Thus, numerous tests have been made to evolve standard tuning curves which provide stretch compensation. These curves are derived by aurally tuning a large number of pianos. The measured frequencies of the aurally tuned notes are then combined to produce average frequencies from which one curve, or at most a limited finite set of curves, are drawn. These curves are unsatisfactory, however, because the actual frequencies are distributed around the average. Thus, if an aurally tuned piano is made to conform to the standard curve, it is, by definition, detuned. Thus, this unique quality of a given piano, i.e., its stretch, which results from its construction, string-length, and myriad other factors, has made the tuning aids practically unworkable in many cases. As a result, the best piano tuners have continued to work conventionally and do not place any significant reliance on these tuning aids.
Therefore, it is an object of this invention to provide a new method for tuning a piano which takes into account the stretch characteristic for that piano.
Another object of this invention is to provide a new method for tuning a piano which enables the use of mechanical aids.
Another objct of this invention is to provide a tuning aid which is readily adapted for tuning a wide variety of instruments.